Question

Approximating Function Values In Exerrises $43-46$ use differentials to approximate the value of the expression. Compare your answer with that of a calculator. $\sqrt[3]{26}$

Name: Problem 44, Chapter 3: Calculus of a Single Variable
Uploaded: 2019-07-30T19:07:15-08:00
Duration: 7 min 1 s
Channel: Carlos Pinilla
Description: Approximating Function Values In Exerrises 43-46 use differentials to approximate the value of the expression. Compare your answer with that of a calculator. √(26)

   Approximating Function Values In Exerrises $43-46$ use differentials to approximate the value of the expression. Compare your answer with that of a calculator.
$\sqrt[3]{26}$

Calculus of a Single Variable

Ron Larson 11th Edition

Chapter 3, Problem 44

Instant Answer

Solved by Expert Carlos Pinilla

07/30/2019

Step 1

The number 27 is a good choice because its cube root is 3. So, we will use 27 as our base point for the linear approximation. Show more…

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Approximating Function Values In Exerrises $43-46$ use differentials to approximate the value of the expression. Compare your answer with that of a calculator. $\sqrt[3]{26}$

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Key Concepts

Differentials

Differentials involve using small changes in the input variable to estimate the corresponding change in the function’s output. This concept is central in calculus for bridging the gap between exact functions and their approximate values through the use of derivatives.

Linear Approximation

Linear approximation, often referred to as tangent line approximation, uses the derivative at a specific point to form the equation of the tangent line. This tangent line is then used to approximate the function values near that point, providing a quick method to estimate values of functions that may be difficult to compute exactly.

Differentiation of Radical Functions

Differentiating radical functions, such as the cube root function, involves leveraging the power rule by rewriting the radical in exponent form. Understanding this concept is crucial for calculating the necessary derivatives to apply differentials for approximation purposes.

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